938 Transactions of the American Institute. 



point of suspension and a point below the center of gravity, the cen- 

 ter of oscillation. You must find this center of oscillation, which 

 requires an exact knowledge of the precise form of the whole struc- 

 ture of the pendulum, and of the density of every part. Then it 

 must be a seconds pendulum, vibrating in a vacuum, at a certain deter- 

 minate level or the result must be reduced to correspond with 

 these conditions. Kater's pendulum has the remarkable property of 

 the exchangeability of its point of suspension and center of oscilla- 

 tion ; and when it is so adjusted that, upon being suspended from 

 either end, the rate of oscillation is precisely the same, the distance of 

 these two points is the exact length of the pendulum. That is cer- 

 tainly very ingenious; but the practical difficulty is, that we must 

 have a seconds pendulum, or a pendulum of an exactly known rate. 

 "We cannot determine the rate of its oscillation with sufficient accu- 

 racy, unless we can attach it to a clock, and allow it to run a long 

 time. Now, we cannot adjust Kater's pendulum in this way ; and if 

 we could, it offers so much resistance to the air, that practically it 

 will not aid us in furnishing a standard for measurement. 



Another proposition is to take for the standard the length of an undu- 

 lation of light. These undulations are very short, but they are very 

 constant ; and if we could ascertain the exact length it would answer 

 the purpose. But the difficulties of measuring these undulations are 

 very great. Their mean length is about 1-50,000 of an inch. The 

 method adopted by Newton for measuring them was exceedingly 

 ingenious. Placing a convex lens on plane glass, colored' rings are 

 formed, which are called Newton's rings. He discovered that they 

 are connected with the distances between the surfaces, and follow a 

 regular law. At the first bright ring the distance is one-fourth of an 

 undulation, or 1-200,000 of an inch. If, then, we know the convexity 

 of the lens and the diameter of the ring, we can calculate the dis- 

 tances of the surfaces. Newton measured the diameter of the ring 

 with dividers, a very clumsy mode, but obtained an extraordinarily 

 close determination of the length of the undulations, agreeing nearly 

 with modern determinations by a more certain method. The measure- 

 ment is now made by means of gitters, consisting of equi-distant lines 

 ruled upon glass ; the length of the undulation being determined by 

 the angle at which the colors are shown, with a certain distance of 

 the lines. But it is necessary that the lines should be exactly equi- 

 distant, and Mr. Rutherford states that it is almost impossible to make 

 a perfect gitter. If there is any error of distance, the error will 



