236 



KNOWLEDGE. 



[OCTOBEB, 1903. 



basic igneous rock, by a siogiilarly pure granite magma, 

 which became locally modified in its ascent. 



We know of no rocks in Ireland older than the invaded 

 series ; but clearly they were laid down under ordinary 

 conditions along a shore. We have nothing left of them 

 in Tirerrlll and Drumahair except the fragments in the 

 gneiss ; but farther north or south their bedded nature is 

 immistakable. One of the critical areas is that above 

 Lough Nafooey, in the County of Galway, where Upper 

 Silurian (Gotlandian) conglomerates contain fragments of 

 the old series, and of a granite also. The granite of 

 southern Galway has not penetrated these Gotlandian beds, 

 though it has highly altered the underlying series of 

 quartzites, schists, and limestones. In other parts of 

 Ireland a granite of similar type has come up along the 

 axes of Caledonian folding, that is. in earliest Devonian 

 times, and has baked and altered the Silurian rocks. 

 Since our ridge in Sligo and Leitrim, continuing the axis 

 of the Ox Mountains, runs parallel with the Caledonian 

 folds, we are left with an open mind as to whether the 

 granite is a very old one remoulded by the Caledonian 

 movements, or an early Devonian one, contemporary with 

 the Leinster Chain.* 



The road from Ballydawley Lough mounts along the 

 south side of the ridge, and the Carboniferous rocks are 

 exposed on our right in little cliffs and quarries. Castle 

 Dargan stands characteristically on a sheer rock above a 

 lake, one of the strongholds which, in this remote district, 

 have an Irish rather than an Anglo-Norman history. 

 Over there in the south, in the passage of the hills beyond 

 Keishcorran, the army of the elder Essex went down before 

 the organised clansmen ; away east at Enuiskillen there is 

 still a certain cleavage between the older races and the 

 newer settlers, who bravely defended what they won. 

 On the north, again, is that delightful folk in Donegal, 

 still speaking Gaelic, a language probably forced upon 

 them by some far-off Celtic overlord. There is no body of 

 men who can be presumed to be primordial in any territory, 

 and least of all in Tirerrill and Drumahair, "where the 

 surge of battle has swept, ever since the stone-age, across 

 the highland-border from the plain. Whose are these 

 long stone graves upon the summits, mined and lichened 

 over before the days of O'Donnells and O'Rourkes? Irish 

 or pre-Irish, they did their best to leave a memory, and 

 were buried where they looked down southward from the 

 hills they called their own. 



And we now climb up past them, past the clean white 

 cottages, with their little flower-gardens, set amid bosses 

 of bare rock, till we come to the townlaud of Correagh, 

 where we pass from Sligo into Leitriui. A green hollow 

 stretches down towards Lough Gill, like a trench cut across 

 the ridge ; in old times the upper part of it was occupied 

 by a lake, the alluvial clay of which forms meadow-laud 

 between the rocks. Lower down, we see that the whole 

 valley depends on the presence of a great dyke of serpen- 

 tine, which has -neathered away, leaving in places a vertical 

 wall of gneiss upon its flank. The outlet of this valley 

 ujion the wooded margin of Lough Gill is one of the 

 surprises of a land where discoveries seem waiting to 

 be made. Perhaps you may find, on some clear sprinc 

 morning, the blue water lapping in simlight round the 

 islands, and the grey crags to northward ledged with 

 newly-fallen snow. 



The gneissic banding of the ridge is magnificently shown 

 on the smooth glaciated surfaces, as we continue along the 

 upland road to Crossboy School. All through this region 

 we find pyroxenites with garnet included in and modifying 

 the igneous invader. Then we pass on to the grass 



• See " The Backbone of LeinBt«r," KyowLEDOE, December, 1902. 



land of the Carboniferous Limestone, the high masses, 

 with scarps and tables, and cliff-set dales like those of 

 Derbyshire, forming a broken background beyond the 

 village of Drumahair. Neglecting the easier route up 

 the Bonet River, we gain the finest contrasts of the 

 country on the old road over the shoulder of Benbo. 

 Lough Gill with its islands stretches from our feet to 

 Sligo city ; the great dome of Knocknarea stands like a 

 fort against the white gleam of the Atlantic, and the 

 woodland climbs towards us from the hollows, breaks into 

 a few stunted fir trees, and vanishes altogether on the 

 grey-green limestone highland. 



The constant washing of these upper slopes has produced 

 at one point a singular brown " coral soil." The limestone 

 has been dissolved away, leaving a mass of coral branches, 

 and a few encrinite stems, as a residue. The fossils stand 

 out also on the exposed surfaces of the rock ; while above 

 rises the heather-clad slope of Benbo, part of the gneissic 

 axis against which the limestone rests. On the bold 

 descent to Manorhamilton, our interest again passes to the 

 gneiss, and the phenomenon of the inclusion of blocks of 

 amphibolite is well seen along the streams. From this 

 point we may turn back to Sligo through Glencar ; or 

 make for the Donegal border across the fine passage of 

 Glenade ; or go east to the lake-country of Enuiskillen, 

 seeing on the way those two Loughs Macnean, which here 

 are taken for granted, but which would be the fortune of 

 any English county. Close to us now, the Shannon rises, ^ 

 imder the sandstone scar of Cuilcagh, and its long course, 

 through chains of lakes, fitly divides this wilder Ireland 

 from the east. 



ConchicUd by M. I. Ceoss. 



NUMERICAL APERTURE AND RAPIDITY. 

 By A. E. CONR.VDY, f.b.a.s., f.r.m.s. 

 The ■' numerical aperture'' by which microscope objectives are 

 usually characterized, and the '■ rapidity " which is marked on 

 ordinary photographic objectives, obviously have some relation 

 to each other, for both increase with the diameter of a lens. 

 The precise nature of this relation is, however, not generally 

 known ; the consequence being that the microscopist who uses 

 a rapid photographic lens for low-power work wonders in vain 

 what " numerical aperture " the instrument possesses, and what 

 resolving power he may reasonably expect from it, whilst the 

 photographer who takes to photomicrography is similarly left 

 in the dark as to the "rapidity " of his complicated apparatus, 

 although that knowledge would be most useful to him in 

 determining the time of exposure required. The following 

 explanation should therefore be acceptable : 



As the rapidity of photographic lenses is usually expressed 

 by /-ratios, such as /8 or ;' IG, we will set our formula to give 

 these ratios, their meaning being that the marginal rays from 

 the lens converge at the nite of 1 in 8 or 16, or whatever the 

 /"-value may be, or at the same rate as those from a simple thin 

 lens of 1 inch diameter and 8 or 16 inches focus. Mathematically 

 the /"-value is therefore determined as the number of times the 

 diameter of the cone of rays, taken at any point, is contained in 

 the distance from that point to the apex of the cone. 



We will now consider a micro3CO])e with au objective of 

 known numerical ajierture, nji., and arranged to give a known 

 magnification X m. The task set us is to find the convergence 

 of the marginal rays on leaving the instrument. 



Let the marginal ray from the object to the lens form an 

 angle a with the optical axis ; and let the same ray, on leaving 



