120 PROCEEDINGS OF THE AMERICAN ACADEMY 



Professor Lovering read a paper on the " Law of Continu- 

 ity," and a seeming exception to it, and illustrated it by va- 

 rious magnetical experiments. 



" The law of continuity supposes that, in the operations of nature, 

 a body passes from one state to another distinct state only by going 

 through all the intermediate states. As to motion, this is obviously 

 true. We cannot conceive of a body getting from one place to an- 

 other, except by moving, in successive instants of time, through the 

 intermediate positions. 



" Leibnitz, who claimed to be himself the originator of this princi- 

 ple, considered it applicable, not only to the position of a body, but to 

 the chemical and physical arrangement of its molecules. He supposed 

 the foundations of this principle to be laid so deep in the arrangements 

 of nature and the structure of the human mind, that man could not, 

 when he reasoned upon the subject, conceive of its non-existence or of 

 any exception to its application. The extreme length to which the law 

 of continuity was pressed by Leibnitz and Bernouilli, in their attempts 

 to demonstrate the laws of mechanics, led Maclaurin and others to 

 reject it altogether. It must be admitted, notwithstanding, that this 

 law of continuity has a firm foundation in truth ; and that, under its 

 guidance, man is put into the right path in the investigation of the plan 

 of nature. The method of analysis which began with Leibnitz and 

 Newton, and which in England has been known under the name of 

 fluxions, rests upon this law of continuity. For it supposes a line to 

 jlow out from a point, a surface from a line, and a solid from a surface ; 

 and this, like any other motion, involves the law of continuity. If we 

 admit the usefulness of the principle only in cases of motion, we still 

 give it a wide range ; since so many problems, not strictly dynamical, 

 are reduced to cases of motion when investigated by the rules of mod- 

 ern analysis. 



" The object of the present communication is not, however, to ex- 

 plain or defend the law of continuity as a sound principle in physical 

 investigation, but to call attention to a few real or apparent exceptions 

 to it with which I have become acquainted in studying the physical 

 forces. 



" If we place a bar-magnet on a table, and move over it lengthwise 

 a small compass-needle which is free to move on a horizontal axis 

 only, when this axis is parallel to the axis of the large magnet, the law 



