144 Major Herschel. On a Simplified Form of the [Dec. 9, 



alteration, being twisted once in 6 inches ; and has a factor of torsion 



equal to 23,700 grs. 



Suppose we decide to use a weight of 200 lbs., so that 



T 2S 700 1 1 1 



— ~ = — nearly. Then r 2 must be greater than or r > — 



P 1,400,000 59 J ° 59?r' 14 



inch. This is so small a limit, that it affords no guide to the best 



value to give to r. 



Again, since 0= — tan 9— — see 9 v^l — cos 2 9 



= +^VT^?=59w**a/ 1-* nearly, 

 A V 2 



it is clear that r must be small, otherwise would be large, and this 

 would demand a great length of wire. We may, indeed, put R = 6~ 



2i7T 



as the least allowable, and this at once gives R = l 77 r 2 , at least. It 

 seems therefore that we must estimate R first. Let us take 3 feet or 



6 



36 inches. This gives r<-y=, or < "45 inch. A smaller value 



v 177 



would give a lower pitch to the twist, which is very desirable. We 

 may therefore take r— 0*4 inch. Whence = 59tt x "16, in terms of 

 59 



radius, or =— X "16— 4*7 revolutions. Finally, tan#=— 0, and 

 .-.9=92° nearly. 



We may sum up the results, so far, as follows : — A weight of 

 200 lbs., suspended by two 0'03 inch steel wires, 36 inches in length, 

 parallel at four-fifths of an inch apart, will be in unstable equilibrium 

 at 92° from its normal position, when the upper ends of the wires 

 have each been turned about their own centres through 4 revolutions 

 250° +92°, or 4 revolutions 342°, from the same normal position. 



In this condition any addition to the weight will tend to strengthen 

 the equilibrium, while, on the contrary, any relief of weight will 

 throw the system over the summit and set it off, allowing it to expend 

 the torsion in twisting the two wires together. 



I will now show how this arrangement may be adapted as a gravi- 

 meter, not so much aiming at a description of a finished instrument 

 as at a sketch of something which will fully illustrate what a more 

 perfect design would fulfil. 



A piece of wire, of the kind described, 7 feet long, is to be twisted 

 upon itself, without straining, giving it ten full turns of torsion, and 

 the ends are then to be secured to each other. This can easily be 

 done so as to give it no chance of relieving itself otherwise than by set, 

 a term which I understand to be the technical one in this connexion, 

 meaning that change which takes place in a wire when it is super- 

 torted or overturned beyond what its elasticity will bear. A wire so 



