146 PROCEEDINGS OF THE AMERICAN ACADEMY. 



unit of torsion. If now we insert these numbers in the above equa- 

 tion and solve for the values of p, which correspond to the various 

 values of the torsion given in the third column of the table, the re- 

 sults given in the last column are obtained. The form of the equation 

 shows that there are two values of 2^ for any particular value of the 

 torsion. If we differentiate (IV) with respect to }) to get the value of 

 p, for which the torsion is a maximum, we get j»^= ^/ A, or/j = 23.1. 

 With the millimeter as the unit this is the same as j9 = 0.116 mm. 

 The value of the torsion for this value of jt? is 254°. The curve indi- 

 cates a maximum where p = 0.120 mm., and its value is 252°. The 

 further discussion of equation (IV) is reserved until more and more 

 accurate data have been collected. 



With the object of rendering the instrument more easily handled, 

 and thus making it susceptible of greater accuracy, it is proposed now 

 to modify the form of the suspended system in order to reduce its mo- 

 ment of inertia. When this has been done the results from this 

 instrument should be quite as reliable as those from the other, and 

 with the experience which has been gained both in constructing and 

 handling the apparatus it seems quite certain that the desired object 

 will soon be accomplished. 



Grateful acknowledgment is made to Professor Trowbridge for plac- 

 ing at my disposal all the resources of the laboratory, including the 

 services of a mechanician ^^ ^nd of a glass-blower. 23 Without the 

 assistance rendered by them the apparatus could not have been con- 

 structed. To Professor Hall, who first called my attention to the 

 problem, I am indebted for much advice and encouragement. 



Jefferson Physical Labouatory, 

 Harvard University. 



22 Mr. Thompson of the Physical Laboratory. 



23 Mr. Oelling. 



