22 F. E. Nvpher — Surfaces of the Compound Pendulum. 



Johannes August Christian Eoeper died on the 17th of 

 March, 1884, at the age of eighty-four. He had been for some 

 time the oldest botanist we know of, at least the oldest boiani- 

 cal author; for his first work, a monograpii of the German spe- 

 cies of Euphorbia, was published in 1824. He was director of 

 the Botanic Garden at Basle in 1828, when he published his 

 classical paper De Orgdnis Plantarum, and he may have been so 

 in 1826, when he contributed to Seringe's Melanges Botaniques 

 his paper on the nature of flowers and of inflorescences, which 

 first put the latter upon a scientific basis and essentially estab- 

 lished the present nomenclature. He was botanical professor 

 there in 1830, when he published his tract De Floribus et Affini- 

 tatibus Balsaminearum . In these essays he gave the promise of 

 being one of the foremost morphological botanists of the age. 

 Some time before the year 1840 he was translated to Eostock, 

 where he held the botanical professorship for more than forty 

 years, but without fulfilling the promise of his youth by 

 additional contributions to the science of any considerable 

 importance. There are, however, some articles from him in 

 the Botanische Zeitung, and other German periodicals, the 

 latest in the year 1859. In 1851 he was chosen a Foreign 

 Member of the Linnean Society of London. We find no record 

 of the place or time of his nativity, but we infer from a state- 

 ment in the preface of his work on Euphorbia, which was pub- 

 lished at Gcettingen, that he was German, and not Swiss. He 

 is said to have been most amiable, and of deep religious convic- 

 tions. 



Art. III. — The Isodynamic Surfaces of the Compound Pendu- 

 lum ;* by Francis E. Nipher. 



In discussing the compound pendulum, the statement is 

 sometimes made, that particles near and below the axis of sus- 

 pension are retarded, and that those near the bottom of the 

 pendulum are accelerated by reason of their connection with 

 the system. The series of particles forming the axis of oscilla- 

 tion are neither accelerated nor retarded. 



In a general way, so far as it concerns the time of a complete 

 oscillation, this is all true, but it is not true in any compound 

 pendulum that the particles near the bottom continually exert 

 a retarding effect upon the system. At any given instant, cer- 

 tain particles in the system tend to diminish the actual accelera- 



*Read before the St. Louis Academy of Science, Oct. I9th, 1885. 



