A. MATHEMATICS AND ASTRONOMY. 5 



can represent it. The simpler inverse problem of describing 

 the curve from the given equation is naturally the first to be 

 undertaken. The forms that thus result may, when com- 

 pared with a given new or unknown curve, suggest the form 

 of the equation that belongs to the latter. In order to pre- 

 sent a number of curves for future study. Professor Newton 

 has therefore selected a single one of the numberless tran- 

 scendental equations, and has in a series of twenty-five plates, 

 embracing one hundred and fifty figures, presented a few of 

 the very many plane curves which this one equation furnish- 

 es. Among the curves figured by him are some which re- 

 duce to a simple series of consecutive rows of isolated dots; 

 others reduce to systems of intersecting straight lines. Other 

 cases represent systems of screws and circles. The more 

 complicated figures present innumerable suggestive and beau- 

 tifully regular patterns, differing entirely in their character- 

 istics from those ordinarily presented by the eccentric lathe, 

 as applied to the ornamentation of bank-notes. Trans. Con- 

 necticut Academy of Sciences^ III., 97. 



dollen's method of determining local time. 



It is well known that the method of determining the time, 

 and consequently the longitude, by the use of the transit in- 

 strument, not in the meridian, but in the vertical of the po- 

 lar star, has long been enthusiastically advocated by Dollen, 

 and the numerous geodesists whom he has instructed at the 

 Imperial Observatory at Poulkova. A short memoir on this 

 subject was published by him in 1864, on the celebration of 

 the twenty-fifth anniversary of the founding of that magnif- 

 icent institution. This memoir subsequently became avail- 

 able to Americans through Mr. Abbe's translation published 

 by the Ilydrographic Bureau of the Navy Department. Dol- 

 len has now published a much more complete treatise, whose 

 appearance has been delayed for various reasons, but by vir- 

 tue of which delay the author states he is enabled now to 

 say with perfect assurance that the method advocated by 

 him has stood every test of experience, and must now be 

 considered as the best that is known. A third memoir is 

 promised by him on the same subject, and will be looked 

 forward to with o-veat interest. His confidence in the ex- 

 cellence of the method of determination of time in the verti- 



