CHAPTER XII. 



MISCELLANEOUS EXPERIMENTS. 

 I. HEAVY GRAVITATIONIAL SYSTEMS. 



107. Attractions in case of a heavy needle. The above gravitational ex- 

 periment had to be discontinued when the steam heat was turned into the 

 building. It seemed worth while, however, to make a few tests with a needle 

 so heavy, that the radiant forces might be small in comparison with the grav- 

 itational attractions. Here, moreover, the air resistances to the motion of 

 the needle could possibly be disregarded, and the excursions, therefore, 

 treated as a case of nearly uniformly varied motion, resulting from gravi- 

 tational attraction. 



108. Apparatus. The apparatus for this purpose had the usual form (fig. 

 178), MM' being two heavy balls of lead, each weighing about 1,500 grams 

 originally. They were counterpoised in suspension from the three-eighths-inch 

 aluminum tube KB', effectively R = 29.3 cm. long. This was supported by the 

 thin brass tube t and brass sleeves, with an appropriate brace of bronze wire b. 

 The torsion- wire w, of thinnest hand-drawn steel (music wire) , was adjustably 

 attached above to a torsion-head, anchored in the pier and below to the tube t . 

 By passing w around the threads of a fine screw above on the torsion-head, the 

 needle could be raised and lowered at pleasure. The length of the wire was 

 154 cm. and its diameter about 0.022 cm. Tested with a variety of brass cylin- 

 ders of known moments of inertia, the torsion coefficient was about r= 154 in 

 the original installment. 



The apparatus was surrounded (except as to the wire w) by a closely fitting 

 glass case. Care was taken to avoid steel or iron in moving parts. The attract- 

 ing mass corresponding to M was on the outside of the case and moved easily 

 on a circular track, as in the earlier work. 



To read off the deflections, a small mirror m, with telescope and scale at a 

 distance of R f = 2go cm. was first adopted. To use the interferometer it was 

 merely necessary to replace m by a silvered strip of thin glass plate; for small 

 additions of weight are here of little consequence. 



Hence the force by which M is drawn from without will be 



r T s 154 



where s is the deflection in centimeters. 



If we estimate the moment of inertia of the needle as 2X1, 500X302 = 2. 7 X 

 io 6 , the period should be about 14 minutes. We may therefore assume that 

 the period will not exceed 15 minutes in interpreting the excursions. 



The gravitational force for an attracting weight of the same value (M = 1,500 

 grams and 6 cm. between centers) would be roughly 



141 



