382 



SCIENCE. 



Sections of this and the Traverse region of Michigan 

 are still sparsely settled, or not at all, and have been visi- 

 ted rarely by botanists. Consequently, we may expect 

 many editions to our flora, as well as corrections, when 

 this region is as thoroughly known as the south half of 

 the State now is ; our ignorance, rather than nature's 

 parsimony, explaining why we have so few species credi- 

 ted to us. The most promising held for the botanist 

 evidently lies in the Houghton Lake region and north- 

 ward, and in the upper Peninsula, many parts of the in- 

 terior of which are botanically unknown. 



Our flora, as here presented, contains in all 113 families 

 (orders), and 1,634 species. The composites claim the 

 largest number of species, 182 — about one-ninth of all. 

 Sedges follow with 176 species; grasses, 139; rosacea;, 

 61 ; ferns, 56; leguminosae, 55 ; figworts, 46; mints, 40; 

 mustard and crowfoot, 39 each ; heath family, 35 ; and 

 umbelliferae, 27. We have 165 trees and shrubs, about 

 20 of which are valuable timber trees. At least 40 of our 

 trees and shrubs are worthy of cultivation for ornament. 

 Sugar maples and elms are commonly planted, while the 

 tulip tree, basswood, Kentucky coffee tree, black walnut, 

 and butternut, among deciduous trees, and hemlock, 

 white pine, black spruce, arbor vita;, and red cedar, 

 among evergreens, deserve more attention. About 20 

 species of woody and herbaceous native climbers are 

 frequent, and some are worthy of cultivation, (see State 

 Pomological Report of '79 for a list.) Ninety medicinal 

 plants are admitted into the U. S. Pharmacopoeia, 45 

 belonging to the primary list, and an equal number to 

 the secondary, while a number of others deserve atten- 

 tion at the hands of Pharmacists. 



It may be stated in conclusion that, in the preparation 

 of this catalogue, we have spared no pains to make it 

 thoroughly reliable, a majority of the species enumerated 

 having passed through our hands, and the remainder be- 

 ing admitted only on good authority. We have pre- 

 ferred to make a useful rather than a a large catalogue, 

 and, on this ground, we have rejected a number of 

 species, some of which may yet make good their claim to 

 be considered as part of our flora. We cannot hope to 

 have escaped all errors, and crave charitable judgment 

 for any such the kind reader may discover, trusting that 

 they may be found errors of omission rather than of com- 

 mission. 



In our arrangement of orders, we have preferred, as 

 more convenient, to follow the 5th edition of Gray's 

 Manual rather than later works. The vexatious subject 

 of synonomy has received considerable attention, and 

 will, we believe, be found brought down nearly to date. 

 Further observations will be published from time to time 

 in the form of addenda, towards increase of which we 

 solicit correspondence and contributions from all parts of 

 the State. 



Ionia, Mich., January 20, 1881. 



DISRUPTION OF PLANETARY MASSES FROM 

 THE PRIMEVAL NEBULA. 



By Edgar L. Larkin. 



It has been shown in this series that the gaseous sphere 

 could not have parted with any form of ring known to 

 geometers. All varieties of segmental rings were exam- 

 ined, and their displacement found impossible by known 

 laws of mechanics. The nebula subsided from space to 

 the dimensions of the orbit of Neptune, else its assumed 

 rotation could not have been equal to the orbital velocity 

 of that planet. 



Indeed, it must have revolved faster, for matter along 

 the line of the centre of gravity of the ring moved with 

 the rate that Neptune now has. Then the outside of the 

 ring moved faster and the inside slower than the Neptu- 

 nian velocity. But the inside was required to move with 

 greater rapidity than any other point to exceed attraction 



and disrupt the mass. From this consideration alone 

 the doctrine of ring detachment is subverted. 



We are now to demonstrate that no particle whatever 

 can be detached from a revolving sphere whether gase- 

 ous, fluid or solid, by any force known to man. Tan- 

 gental force in no case overcomes radial, being unable 

 from known physical laws, which teach that not an atom 

 ever left a rotating cosmical mass. We have made cal- 

 culation of the maximum effect ot tangental force on 

 matter on the equator of the sphere when coincident with 

 the orbit of Neptune, radius being 2,780,000,000 miles. 

 And if the solar parallax is modified, bringing Neptune 

 somewhat nearer, the figures will not be in material er- 

 ror. It is a law of mechanics that if matter is thrown 

 off the periphery of a revolving sphere by force evolved 

 by rotation, the detached portion always, when maximum 

 power is exerted, traverses a line tangent to the curva- 

 ture at the point of departure. If a revolving globe 

 should burst, the pieces would be projected along tan- 

 gental lines and never rise higher. But what is a tan- 

 gent to the Neptunian orbit, and what is its departure 

 from the curvature of that mighty sphere whence Nep- 

 tune's mass is said to have been detached ? It is apos- 

 tulate of the Hypothesis that the nebula was a sphere, 

 else it could not have parted with matter in the form of a 

 ling. We adopt the idea that it was round, and for the 

 purposes of trigonometry imagine the surface to have 

 been as level as still water. We are in search of the de- 

 parture of the tangent from the curve at different dis- 

 tances along the equator, to learn how far tangental force 

 was able to project matter above the periphery. 



The length of 1" of arc on the equator of the nebula 

 was 13,478 miles, and we made selection of 8" of arc or 

 107,824 miles to find the amount of its deflection from 

 the tangent. The curvature cannot be detected by tables 

 of logarithmic functions carried to the sixth decimal 

 place — thus : 



log. sin. 1' = 6.463726 

 log. 60 = 1. 7781 51 



log. sin. 1 ' 

 log. 8 



log. sin. 8" 



and 

 log. tan. 1" 

 log. 8 



= 4-685575 

 = -903090 



= 5.588665 



= 4-685575 

 = .903090 



log. tan. 8" = 5.588665 



That is, the logarithmic sine and tangent of 8" are the 

 same ; hence the arc cannot be told from a straight line 

 by ordinary tables. This being the case, radii drawn to 

 the centre from each extremity would be equal in length, 

 and it follows that any particle of matter on the equator 

 of the primeval sphere, after having traversed more than 

 a hundred thousand miles under the influence of tan- 

 gental force, was no further from the centre than when 

 it started, making the formation of a ring, or detachment 

 of an atom, alike impossible. 



Not deeming it true that an arc of such length had no 

 curvature, and not having logarithmic tables for exact 

 computation of functions near their limits, we were 

 obliged to use the cumbersome method of natural sines, 

 cosines and tangents, carrying the calculation to the 

 twentieth decimal place to secure accuracy. 



To find the cosines of such minute arcs use was made 

 of the formula — Cos. = i — y z sin. 2 , and for secants — 



Sec A= C ^A. 



Applying these formula; to the arc of 8" it was found 

 that the secant was only 1.94 miles longer than the 

 radius. That is, the curvature of the sphere at any 

 point distant 107,824 miles from another, made a point 

 of tangency, is less than two miles ! Let us watch the 

 career of an atom destined to be cast off' the equator to 



