Februaky 1, 1894.] 



KNOWLEDGE 



31 



the observations were free from this. The effect of the 

 leaden spheres on the arm was found to increase or 

 diminish with standing, and this was found to be due to a 

 difi'erence of temperature between the weights and the 

 case. In the first experiments made, the wire by which 

 the arm was suspended was thirty-nine and a quarter 

 inches long ; its material was copper coated with silver. 

 Its stiiiness was such as to make the arm perform a vibra- 

 tion in about fifteen minutes. In the first observations 

 the rods by which the leaden weights were suspended 

 were of iron, but care was taken that there was nothing 

 possessing magnetic properties in the arm. In later 

 experiments the iron rods were replaced by copper, but no 

 change in the observations was caused. Another series of 

 observations was also made, using a stiffer wire. The 

 force required to draw the arm aside, in opposition to the 

 force of restitution in the twisted fibre, was found by 

 observing the time of a vibration and calculating from 

 this. 



The following may serve as an example of the observa- 

 tions made : — 



ilotion of the nrm on inovinu weights from 



positive position to middle position... ... = 15'22 



ilotiou of the ai'm on moviiifr weights from 



middle position to positive position... ... =140 



Time of one vibration when in middle position... = 14-m. 39s. 

 ,, .. .. positive position... =14ni. .54-5. 



The positive and negative positions were those in which 

 the leaden sphere tended to cause a twist in one direction 

 and in the other respectively. The middle position was 

 that in which the spheres were on the line bisecting the 

 middle of the arm. 



The density of the earth was deduced from the observa- 

 tions by comparing the force of attraction of the leaden 

 weights on the balls suspended from the arm with the 

 force of attraction of the earth on the same balls — that is, 

 with their weight. The question is : What must the 

 mass of the earth be when it attracts a ball on its surface — 

 that is, four thousand miles from its centre — with a force 

 greater in a known ratio than that with which the same 

 ball is attracted by a sphere of lead of known mass, 

 placed at a measured distance '? Knowing the law of 

 gravitation, that masses attract each other with a force 

 varying as the product of their masses, and inversely as 

 the square of the distance apart of their centres of gravity, 

 we at once find what the mass of the earth must be, and 

 this divided by the volume of the earth gives its mean 

 density. 



The corrections which Cavendish had to apply to his 

 observations were : — 



1. For the effect which the resistance of the arm to 

 motion had on the time of vibration. 



'2. For attraction of the weights on the arm itself. 



3. For their attraction on the farther ball. 



4. For the attraction of the copper rods on the balls 

 and arm. 



5. For the attraction of the case on the balls and arm. 

 G. For the alteration of the attraction of the weights on 



the balls according to the position of the arm, and the 

 effect which this had on the time of vibration. 



The last correction was of the most importance ; the 

 others did not affect the result much. 



Cavendish says : — " By a mean of the experiments made 

 with the wire first ufed, the density of the earth comes 

 out 5'-18 times greater than that of water ; by a mean of 

 those made with the latter wire it comes out the same. 

 The extreme results did not differ from the mean by more 

 than one-fourteenth of the whole, and therefore the density 

 •should seem to be determined hereby to great exactness." 



The value thus found differs but little from the latest 



determinations made by simOar methods. Prof. Poynting's 

 result (which I will refer to later) obtained quite recently, 

 after great precautions were taken to secure accuracy, is 

 5-498. It is noteworthy that the guess made by Newton 

 in the century preceding Cavendish's experiment, for the 

 density of the earth, namely, five to six times the density 

 of water, is remarkably near that which seems to be the 

 value as determined by the best method. 



The operation of weighing is so familiar to all that many 

 are apt to forget what is actually done when anything is 

 weighed. The method of weighing is adopted as a ready 

 and easy means of finding the mass of a body — that is, the 

 quantity of matter in it. This is done by comparing the 

 attraction of the earth on the body in question with its 

 attraction on another piece of matter whose mass is known. 

 When the masses in the two scale pans of a balance are 

 equal the mass of the earth attracts them equally, and 

 the beam of the balance stands horizontally ; the balance 

 is in equilibrium, and the substances in the two pans are 

 said to be of equal weight. But the attraction of the earth 

 on a mass near its surface depends on the distance of that 

 mass from the centre of the earth, so that a pound has 

 less weight at the top of a mountain than in the valley 

 below. The weights of bodies vary according to their 

 position on the earth's surface, and the same mass has a 

 greater weight at the poles than at the equator, because in 

 the former place it is nearer to the centre of the earth, and 

 the earth's attraction for bodies outside it is the same as if 

 the whole mass of the earth were concentrated at its 

 centre. 



Again, at the equator the motion of the earth about its 

 axis tends to cause a body to fly away from the axis and 

 to decrease the weight of the body. Thus the weight of a 

 body, far from being a constant quantity, varies as the body 

 is moved from place to place. Nevertheless, the method 

 of weighing is an accurate way of determining the amount 

 of matter in a given body, because by this operation we 

 simply compare two attractions, and the forces of attraction 

 on the body and on the standard weights with which it is 

 compared vary equally as the balance is moved from one 

 position to another ; thus, although a body is lighter at 

 the equator, so also is the standard pound against which 

 we compare it. 



The comparison of weights is simple and familiar 

 enough, but can we weigh the earth itself or find its mass? 

 What can we compare it with ? Here, again, what is to 

 be done is to compare two attractions. If we can find the 

 attraction of some mass — a part of the earth — on another 

 mass, and then compare this attraction with that of the 

 earth on the same mass — that is, with its weight — the 

 problem is solved. 



Several methods have been suggested for doing this. 

 Perhaps the earliest attempt was that made by some 

 French geographers, who observed by what amount the 

 plumb line was deflected from the vertical owing to the 

 attraction of a neighbouring mountain. This experiment 

 was performed near Quito, in the Andes, but the observa- 

 tions were but rough and inaccurate ; the deflection 

 seemed to be quite noticeable, but the observations were 

 taken in a tent, and it would be impossible under such 

 conditions to guard properly against currents of air, which 

 would disturb the instrument. 



Later, the suggestion that this method of the plumb 

 line should be used to find the earth's density, by taking 

 observations near some suitably shaped mountain in the 

 British Isles, was made to the Royal Society by Maskelyne, 

 the Astronomer -Pioyal of that time. Schehallien, a 

 mountain in the Scottish Highlands, was finally fixed 

 upon, and the operation carried out there, the re.sults 



