in certain cases, into an arithmetical progression. Thus, having the 

 theorem that N can be resolved into an arithmetical progression 

 when 16 N+l is a square, he is enabled to detect factors in N ; he 

 thus shows that 2079519603 has 43 and 101 among its factors. 

 Among theorems which the method gives, may be noticed the 

 following, as one of a peculiar and unstudied class. If in the series 

 1, 3, 5, 7, &c. four terms be taken, and the next one omitted, then 

 the four next terms taken and the next three omitted, then four 

 terms taken and/#6> omitted, and so on, the four terms taken will 

 in every case consist of numbers prime to one another. 



II. Abstract of a Memoir "On the Electric Properties of 

 Insulating or Non-conducting Bodies/' By Professor 

 CARLO MATTEUCCI of Pisa. Communicated by Major- 

 General SABINE, E.A., V.P. and Treas. R.S. Received 

 April 14, 1859. 



The object of the author in the first part of this memoir is to 

 ascertain by experiment what condition is assumed by insulating or 

 non-conducting bodies in the presence of an electrified body, and in 

 what degree such condition is developed in insulating bodies of 

 different kinds. In a memoir published nearly ten years ago (Ann. 

 de Chim. et de Phys., xxvii. p. 134), he had shown that a cylinder of 

 gum-lac, sulphur, stearic acid, or the like, suspended by a filament 

 of silk, and brought near to a body charged with electricity, begins 

 to oscillate in the same way as a cylinder of metal. The non-con- 

 ducting cylinder, whilst under the influence of induction, behaves 

 like any body charged with opposite electricities, and returns to its 

 natural state when the induction ceases. 



These experiments have now been very carefully repeated with 

 cylinders formed of various insulating substances, made as nearly as 

 possible of the same length and perfectly diselectrized. The air was 

 rendered perfectly dry, and the inducing ball was charged with 

 electricity to a constant degree, measured by the torsion-balance. 



After giving a numerical statement of the time of oscillation and 

 the moment of the induced force, as determined by experiment for 

 cylinders of different insulating substances, and after describing other 



